# Research on instantaneous optimal control of the hybrid electric vehicle with planetary gear sets

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## Abstract

Power-split hybrid electric vehicle (HEV), mainly adopting the planetary power coupling mechanism, is superior in improving the fuel economy because the engine speed and torque are decoupled from those of the wheels. Focusing on a power-split HEV with dual-planetary gear sets, this paper establishes an instantaneous optimal control to regulate its power flow. Firstly, simulation-oriented models are established, including the coupling mechanism, the engine, the electrical machines and the battery. Secondly, feasible operation modes of the vehicle are analyzed. Also, the torque and speed equations between the engine and motors are obtained. On the basis of the above, the instantaneous optimization strategy, adaptive equivalent fuel consumption minimization strategy (A-ECMS), is designed, which is developed from the equivalent fuel consumption minimization strategy. The optimization strategy is of high robustness to different driving cycles. To realize the engine speed tracking, a PI controller is introduced. At last, the control effects of A-ECMS are compared with the effects of the engine optimal operating line control strategy. The effectiveness and rationality of two strategies are tested in the dSPACE real-time simulator. Test results under different driving scenarios prove that the A-ECMS is of better performance in ensuring the HEV fuel economy and the battery charging sustainability.

## Keywords

Power-split HEV Planetary power coupling mechanism Energy management A-ECMS## Abbreviations

- A-ECMS
Adaptive equivalent minimization fuel consumption strategy

- C1
Carrier gear of the first planetary gear set

- C2
Carrier gear of the second planetary gear set

- ECMS
Equivalent minimization fuel consumption strategy

- GM
General motors

- HEV
Hybrid electric vehicle

- HIL
Hardware in the loop

- IO
In/out interface

- MG1
Electric machine 1

- MG2
Electric machine 2

- NEDC
New European Driving Cycle

- OOL
Engine optimal operation line

- P1
The first planetary gear set

- P2
The second planetary gear set

- PMP
Pontryagin’s minimum principle

- R1
Ring gear of the first planetary gear set

- R2
Ring gear of the second planetary gear set

- S1
Sun gear of the first/second planetary gear set

- S2
Sun gear of the second planetary gear set

- SOC
Battery state of charge

- SUV
Sport utility vehicle

- THS
Toyota hybrid system

- UDDS
Urban Dynamometer Driving Schedule

## List of symbols

*A*Vehicle frontal area

*C*_{D}Air drag coefficient

*C*_{p}Correction factor

*F*_{1}Internal force on the pinion gear

*F*_{2}Internal force on the pinion gear

*f*Coefficient of rolling resistance

*I*_{eng}Lumped inertia of the engine

*I*_{fd}Lumped inertia of the main reducer

*I*_{MG1}Lumped inertia of MG1

*I*_{MG2}Lumped inertia of MG2

*I*_{w}Wheel inertia

*I*_{Batt}Battery output current

*I*_{SOC}Correction current

*i*_{0}Ratio of the final drive

*K*_{1}Characteristic parameter of P1

*K*_{2}Characteristic parameter of P2

*k*Discrete time point

*m*Vehicle mass

- \(\dot{m}_{\text{Batt}}\)
Battery equivalent fuel consumption rate

- \(\dot{m}_{\text{eng}}\)
Engine fuel consumption rate

*P*_{eng}Engine power

*P*_{eng_max}Engine maximum power

*P*_{MG1}MG1 power

*P*_{MG1_max}MG1 maximum power

*P*_{MG2}MG2 power

*P*_{MG2_max}MG2 maximum power

*P*_{req}Required driving power

*P*_{b}Battery power

*Q*Battery capability

*Q*_{lhv}Low heat value of gasoline

*R*_{w}Wheel radius

*R*_{in}Battery internal resistance

*r*_{1}Radius of R1

*r*_{2}Radius of R2

- \({\text{S}}\mathop {\text{O}}\limits^{.} {\text{C}}\)
Derivative of battery SOC

- SOC
_{min} Lower limit of the battery SOC

- SOC
_{max} Upper limit of the battery SOC

- SOC
_{ref} Reference SOC

- SOC
_{hist} Final battery SOC

*s*_{1}Radius of S1

*s*_{2}Radius of S2

*s*Equivalence factor

*s*_{chg}Charging equivalence factor

*s*_{dis}Discharging equivalence factor

*T*_{eng}Engine torque

*T*_{eng_min}Minimum torque of the engine

*T*_{eng_max}Maximum torque of the engine

*T*_{MG1}MG1 torque

*T*_{MG1_min}Minimum torque of MG1

*T*_{MG1_max}Maximum torque of MG1

*T*_{MG2}MG2 torque

*T*_{MG2_min}Minimum torque of MG2

*T*_{MG2_max}Maximum torque of MG2

*T*_{req}Required torque

*T*_{out}Load torque

*T*_{f}Friction braking torque

*T*_{eng_ideal}Ideal engine torque

*T*_{1}Internal torque between MG1 and S1

- \(T_{1}^{'}\)
Internal torque between MG1 and S1

*T*_{2}Internal torque between MG2 and S2

- \(T_{2}^{'}\)
Internal torque between MG2 and S2

*T*_{3}Internal torque between the engine and C1

- \(T_{3}^{'}\)
Internal torque between the engine and C1

*t*_{f}Time of a selected fragment

*V*_{oc}Battery open-circuit voltage

*V*_{Batt}Load voltage

*x*_{SOC}Correction SOC

*ω*_{eng}Engine speed

*ω*_{eng_min}Minimum speed of the engine

*ω*_{eng_max}Maximum speed of the engine

*ω*_{MG1}MG1 speed

*ω*_{MG1_min}Minimum speed of MG1

*ω*_{MG1_max}Maximum speed of MG1

*ω*_{MG2}MG2 speed

*ω*_{MG2_min}Minimum speed of MG2

*ω*_{MG2_max}Maximum speed of MG2

*ω*_{out}Output speed of the power coupling device

*ω*_{eng_ideal}Ideal engine speed

*ω*_{eng_act}Actual engine speed

*η*_{MG1}Efficiency of MG1

*η*_{MG2}Efficiency of MG2

*η*_{chg}Charging efficiency of the battery

*η*_{dis}Discharging efficiency of the battery

*ϕ*_{1}Map for MG1 efficiency

*ϕ*_{2}Map for MG2 efficiency

*Γ*Map for engine fuel flow rate

*ρ*Air density

*ψ*State factor

*γ*_{SOC}Weight factor

## Notes

### Acknowledgements

This study was supported by the National Nature Science Foundation of China (Grant Nos. 51475213, U1764257), the Foundation for Jiangsu Key Laboratory of Traffic and Transportation Security (Grant No. TTS2018-01) and the ‘333 Project’ of Jiangsu Province (BRA2018178).

## References

- 1.Chen L, Zhu F, Zhang M, Huo Y, Yin C, Peng H (2011) Design and analysis of an electrical variable transmission for a series–parallel hybrid electric vehicle. IEEE Trans Veh Technol 60(5):2354–2363CrossRefGoogle Scholar
- 2.Cipek M, Pavković D, Petrić J (2013) A control-oriented simulation model of a power-split hybrid electric vehicle. Appl Energy 101(1):121–133CrossRefGoogle Scholar
- 3.Kang J, Choi W, Kim H (2012) Development of a control strategy based on the transmission efficiency with mechanical loss for a dual mode power split-type hybrid electric vehicle. Int J Automot Technol 13(5):825–833CrossRefGoogle Scholar
- 4.Ahmadizadeh P, Mashadi B (2016) Power flow and efficiency analysis of the EM power split mechanism. J Braz Soc Mech Sci Eng 39:1947–1955CrossRefGoogle Scholar
- 5.Jin Y, Wu C, Hu Y et al (2016) Characteristic analysis of a new compound HMCVT. J Jiangsu Univ Nat Sci Ed 37(5):507–511Google Scholar
- 6.Burress TA, Campbell SL, Coomer C, Ayers CW, Wereszczak AA, Cunningham JP (2011) Evaluation of the 2010 Toyota Prius hybrid synergy drive system. Office of scientific & technical information technical reportsGoogle Scholar
- 7.Grewe TM, Conlon BM, Holmes AG (2007) Defining the general motors 2-mode hybrid transmission. In: SAE world congress & exhibitionGoogle Scholar
- 8.Wishart JD, Zhou L, Dong Z (2008) Review, modelling and simulation of two-mode hybrid vehicle architecture. Am Soc Mech Eng 3:1091–1112Google Scholar
- 9.Shi D, Wang S, Pisu P, Chen L, Wang R, Wang R (2017) Modeling and optimal energy management of a power split hybrid electric vehicle. Sci China Technol Sci 60(5):713–725CrossRefGoogle Scholar
- 10.Taghavipour A, Azad NL, Mcphee J (2015) Design and evaluation of a predictive powertrain control system for a plug-in hybrid electric vehicle to improve the fuel economy and the emissions. Proc Inst Mech Eng Part D J Automob Eng 229:624–640CrossRefGoogle Scholar
- 11.Bayindir KÇ, Gözüküçük MA, Teke A (2011) A comprehensive overview of hybrid electric vehicle: powertrain configurations, powertrain control techniques and electronic control units. Energy Convers Manag 52(2):1305–1313CrossRefGoogle Scholar
- 12.Panday A, Bansal HO (2014) A review of optimal energy management strategies for hybrid electric vehicle. Int J Veh Technol 2014:1–19CrossRefGoogle Scholar
- 13.Yang H, Kim B, Park Y, Lim W, Cha S (2009) Analysis of planetary gear hybrid powertrain system part 2: output split system. Int J Automot Technol 10(3):381–390CrossRefGoogle Scholar
- 14.Enang W, Bannister C (2017) Modelling and control of hybrid electric vehicles (a comprehensive review). Renew Sustain Energy Rev 74:1210–1239CrossRefGoogle Scholar
- 15.Kim N, Cha SW, Peng H (2012) Optimal equivalent fuel consumption for hybrid electric vehicles. IEEE Trans Control Syst Technol 20(3):817–825CrossRefGoogle Scholar
- 16.Škugor B, Cipek M, Deur J, Pavković D (2014) Design of a power-split hybrid electric vehicle control system utilizing a rule-based controller and an equivalent consumption minimization strategy. Proc Inst Mech Eng Part D J Automob Eng 228(6):631–648CrossRefGoogle Scholar
- 17.Kim N, Cha S, Peng H (2011) Optimal control of hybrid electric vehicles based on pontryagin’s minimum principle. IEEE Trans Control Syst Technol 19(5):1279–1287CrossRefGoogle Scholar
- 18.Serrao L, Onori S, Rizzoni G (2011) A comparative analysis of energy management strategies for hybrid electric vehicles. J Dyn Syst Meas Control 33(3):031012CrossRefGoogle Scholar
- 19.Taghavipour A, Vajedi M, Azad NL, Mcphee J (2016) A comparative analysis of route-based energy management systems for phevs. Asian J Control 18(1):29–39MathSciNetzbMATHCrossRefGoogle Scholar
- 20.Feng T, Lin Y, Gu Q, Hu Y (2015) A supervisory control strategy for plug-in hybrid electric vehicles based on energy demand prediction and route preview. IEEE Trans Veh Technol 64(5):1691–1700CrossRefGoogle Scholar
- 21.Pisu P, Rizzoni G (2007) A comparative study of supervisory control strategies for hybrid electric vehicles. IEEE Trans Control Syst Technol 15(3):506–518CrossRefGoogle Scholar
- 22.Sun C, Sun F, He H (2017) Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy 185:1644–1653CrossRefGoogle Scholar
- 23.Onori S, Serrao L, Rizzoni G (2010) Adaptive equivalent consumption minimization strategy for hybrid electric vehicles. In: ASME 2010 dynamic systems and control conference, pp 499–505Google Scholar
- 24.Li CT, Zhang X, Peng H (2012) Design of power-split hybrid vehicles with a single planetary gear. In: ASME 2012 5th annual dynamic systems and control conference joint with the JSME 2012 11th motion and vibration conference. American Society of Mechanical Engineers, pp 857–865Google Scholar
- 25.Yan F, Wang J, Huang K (2012) Hybrid electric vehicle model predictive control torque-split strategy incorporating engine transient characteristics. IEEE Trans Veh Technol 61(6):2458–2467CrossRefGoogle Scholar
- 26.Xiong J, Gu H (2017) An intelligent dual-voltage driving method and circuit for a common rail injector of heavy-duty diesel engine. IEEE Access 99:1CrossRefGoogle Scholar
- 27.Long C, Hao R, Yuan C, Wang S, Sun X, Li D (2015) Design and simulation power system for hybrid electric vehicles with wheel motors. J Jiangsu Univ Nat Sci Ed 36(1):6–10Google Scholar
- 28.Huang W, Cheng Y, Cao H, Wang H (2013) Matching experiment of EV power-train parameters. J Jiangsu Univ Nat Sci Ed 34(2):131–137Google Scholar
- 29.He H, Xiong R, Fan J (2011) Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies 4(4):582–598CrossRefGoogle Scholar
- 30.Muyi L, Zhongjie Yu, Li Z, Yong C (2018) Working cycle identification: based braking control strategy and its application for hydraulic hybrid loader. Adv Mech Eng 10(5):1–12Google Scholar
- 31.Borhan H, Vahidi A, Phillips AM, Kuang ML, Kolmanovsky IV, Cairano SD (2012) Mpc-based energy management of a power-split hybrid electric vehicle. IEEE Trans Control Syst Technol 20(3):593–603CrossRefGoogle Scholar
- 32.Zhu F, Chen L, Yin C (2013) Design and analysis of a novel multimode transmission for a hev using a single electric machine. IEEE Trans Veh Technol 62(3):1097–1110CrossRefGoogle Scholar
- 33.Zhuang W, Zhang X, Ding Y, Wang L, Hu X (2016) Comparison of multi-mode hybrid powertrains with multiple planetary gears. Appl Energy 178:624–632CrossRefGoogle Scholar
- 34.Ghafouryan MM, Ataee S, Dastjerd FT (2016) A novel method for the design of regenerative brake system in an urban automotive. J Braz Soc Mech Sci Eng 38(3):945–953CrossRefGoogle Scholar
- 35.Yazdani A, Shamekhi AH, Hosseini SM (2015) Modeling, performance simulation and controller design for a hybrid fuel cell electric vehicle. J Braz Soc Mech Sci Eng 37(1):375–396CrossRefGoogle Scholar
- 36.Shi D, Pisu P, Chen L, Wang S, Wang R, Yan J (2016) Control design and fuel economy investigation of power split HEV with energy regeneration of suspension. Appl Energy 182:576–589CrossRefGoogle Scholar